Question: Simplify the following expression: $y = \dfrac{72r^2 + 24r}{-16r^2 - 48r}$ You can assume $r \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $72r^2 + 24r = (2\cdot2\cdot2\cdot3\cdot3 \cdot r \cdot r) + (2\cdot2\cdot2\cdot3 \cdot r)$ The denominator can be factored: $-16r^2 - 48r = - (2\cdot2\cdot2\cdot2 \cdot r \cdot r) - (2\cdot2\cdot2\cdot2\cdot3 \cdot r)$ The greatest common factor of all the terms is $8r$ Factoring out $8r$ gives us: $y = \dfrac{(8r)(9r + 3)}{(8r)(-2r - 6)}$ Dividing both the numerator and denominator by $8r$ gives: $y = \dfrac{9r + 3}{-2r - 6}$